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Abstract— In this paper, we propose a trajectory-adjustable
integrated milli-scale jumping-crawling robot with improved
ability to overcome obstacles compared to a robot that can only
crawl. The robot employs a novel jumping module with
enhanced energy storing-capacity and a height-adjustable active
trigger. To increase the energy-storing capacity, latex rubber
and knee-like joints are employed to utilize large displacement
of the elastic material. The active trigger is based on a single DC
motor and can release stored energy at any state, enabling the
robot to control the take-off speed of jumping. The jumping
module is integrated with the lightweight Dash crawler. The
integrated jumping-crawling robot weighs 59.4 g and controls its
moving trajectory by adjusting both its crawling speed and its
jumping take-off speed.
I. INTRODUCTION
Recent research on mobile milli-scale robots has focused
on increasing their maneuverability by changing from single
locomotion modes such as jumping, crawling, and climbing
to forms of locomotion that integrate multiple movements
(termed multi-modal locomotion). Milli-scale robots with
multi-modal locomotion have been developed for two
applications: reducing the cost of transport (CoT) and
expanding locomotion domain.
Robots developed to reduce CoT combine jumping and
gliding, “jump-gliding”. [4-8]. Jump-gliding enables these
robots to travel an extended horizontal distance for a given
amount of stored energy. These robots can also achieve
various trajectories and land on the ground gently.
Robots developed to expand locomotion domain often use
an integrated crawling and jumping locomotion method [2, 9-
12]. The same integrated crawling-jumping locomotion can
easily be seen in small insects such as locusts, grasshoppers
and froghoppers. During ordinary locomotion, these insects
mainly use their four fore-legs to walk and crawl. But to escape
from predators and to reach places where they cannot crawl,
they use their relatively long and thick hind legs.
Inspired by such insects, milli-scale robots that use both
crawling and jumping locomotions have been developed.
Stoeter et al. [2] proposed a Scout robot that has two wheels
for rolling and a winch for jumping into three-dimensional
(3D) space. The robot can jump up to 30 cm by using its
spring steel foot. While the Scout robot employs separate
jumping and rolling motions, the Mini-WhegsTM robot
* This research was supported by a grant to Bio-Mimetic Robot Research
Center, funded by Defense Acquisition Program Administration under the grant number UD130070ID.
G. P. Jung, S. P. Jung, and K. J. Cho are with the Biorobotics Laboratory,
School of Mechanical & Aerospace Engineering/IAMD, Seoul National University, Seoul, Republic of Korea.
developed by Lambrecht et al. [12] uses integrated running
and jumping motions. The robot overcomes obstacles by
jumping up to 18 cm (1.76 J/kg) while also crawling. These
robots have successfully suggested the feasibility of
expanding reachable domain by integrating crawling and
jumping.
In this paper, we propose a robot that can control its
trajectory by adjusting both its crawling speed and its jumping
take-off speed. The robot consists of a height-adjustable and
powerful jumping mechanism that is integrated with the
lightweight six-legged Dash crawler (Dash Robotics Inc.). The
whole robot weighs 59.4 g and is shown in Fig. 1. Because the
robot can jump from 1.10 m to 1.62 m and crawl at a speed of
0 m/s to 0.62 m/s, it can follow various trajectories of
movement.
The paper is organized as follows: The design section
describes the structure of the mechanism, material selection,
and how we maximized the mechanism’s energy-storing
capacity. The modeling section considers both static and
Carlos S. Casarez and Ronald S. Fearing are with the Department of
Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA. (corresponding author: 82-2-880-1703, fax: 82-
2-880-1663, [email protected])
An Integrated Jumping-Crawling Robot using Height-Adjustable
Jumping Module
Gwang-Pil Jung, Carlos S. Casarez, Sun-Pill Jung, Ronald S. Fearing and Kyu-Jin Cho, Member,
IEEE
Fig. 1. The 59.4g integrated jumping-crawling robot in (a) the fully
loaded stated and (b) the released stated.
TABLE I. EXISTING JUMPING-CRAWLING ROBOTS
Robots Mass
(g)
Size
(cm)
Jumping
height (m)
Jumping
distance (m)
Scout [2] 200 11.5 0.57 -
MiniWheg [12] 191.4 10.4 0.18 -
Proposed robot 59.4 10.0 1.62 0.6
dynamic modeling of the loading force and dynamic motion of
the jumping mechanism. The experiments section describes
the results of experiments to assess the robot’s ability to
overcome obstacles.
II. JUMPING MODULE DESIGN
The jumping module is developed to satisfy two design
requirements. First, the jumping module needs to have an
energy-storing capacity of more than 46.7 J/kg (1.4 J in 30.0
g module) to allow the whole system to jump to height of 2m,
assuming that the mass of the whole system is about 60.0g.
The value of 46.7 J/kg is quite large amount in milli-scale
jumping robots. To our knowledge, a 7 g jumping robot [14]
has energy-storing capacity of about 21.9 J/kg, which is the
largest amount of stored energy among current milli-scale
robots.
To increase energy-storing capacity, our approach begins
with the basics. Fig. 2 shows two structures that have a force
limit of kx, where k is the spring constant and x is the
displacement. The structure in Fig. 2 (a) stores the energy of
3kx2/2 while the structure in Fig. 2 (b) stores kx2/2. This
suggests that large displacement rather than large spring
constant can increase energy-storing capacity. To implement
this basic principle, we employ a hyperelastic material to
utilize large strain of the material. We also employed a fully
compressible linkage shown in Fig. 2 (a) and a knee-like joint
to easily lengthen the material (shown in Fig. 6).
The second design requirement is that the jumping module
should be able to actively release the stored energy,
irrespective of the quantity of energy stored, to control the
take-off speed of jumping. To this end, a novel active
triggering mechanism based on a single DC motor is designed.
A. Energy Storing Material
Spring steel has been widely employed for energy-storing
components due to its easy accessibility. However, according
to [15], spring steel is not a very efficient energy-storing
material because of its high density. Instead of spring steel, we
employ rubber material in the jumping module since it has an
outstanding energy density compared to other materials [15].
However, rubber generally shows large hysteresis in its force-
displacement curve. Table II shows the properties of five
possible materials. Polyurethane has high energy density but
also a high loss factor [1]. In contrast, latex has relatively low
energy density and modulus but can be stretched by more than
250% and has small hysteresis in its force-displacement curve
[1], as shown in Fig. 3. Latex therefore fit our design
requirement to maximize energy-storing capacity.
B. Structure of the Jumping Module
The structure of the jumping module utilizes a simple
diamond-shaped four-bar linkage to lengthen the latex as
shown in Fig. 4. As the structure is compressed, the latex
stretches and the amount of stored energy increases. Fig. 4 (a)
shows the mechanism with a full load of stored energy, and
Fig. 4. Conceptual models of the proposed jumping mechanism in (a) the fully loaded state, (b) the released state, and (c) the one-third loaded state. The
mechanism can jump from both the fully loaded state and the one-third loaded state depending on the required jumping heights
Fig. 2. Storable energy depends on the spring constant and
displacement, assuming that both structures have the same force limit,
𝐹 = 𝑘𝑥.
TABLE II. MATERIAL PROPETIES [1]
Materials Young’s
Modulus
(GPa)
Energy
/Vol
(mJ/mm3)
Energy
/Mass
(J/kg)
Dissipation
factor at
1kHz
Silicon 190 0.66 280 -
Resilin 0.002 2.25 2100 -
PDMS 0.00075 3.3 3400 -
Polyurethane 0.0076 95 76000 0.034
Latex 0.0001 5 4000 0.005
Fig. 3. Experimental results of stretching latex. The specimen is 5.5
mm wide, 25 mm long, and 0.85 mm thick.
Fig. 4 (c) shows it at one-third of its full capacity. The stored
energy is released by decompressing the structure, as shown in
Fig. 4 (b).
Fig. 5 (c) shows the 3D CAD model of the entire jumping
module. A pair of wires is attached at both sides, and a pulley
winds the wires to compress the structure. When this occurs,
the routed latex rubber stretches and stores energy, as shown
in Fig. 5 (d).
C. Roll and Slide Joints with Crossed Flexures
The degree to which the jumping structure can be
compressed basically depends on the range of motion of its
joints. If the joints have little range of motion, then the
structure cannot be fully compressed or decompressed. To
solve this issue, we developed a rolling and sliding joint
inspired by the human knee, as shown in Fig. 6 [16].
The joint shown in Fig. 6 (a) can be fully folded and
unfolded, just like the human knee. The joint consists of three
crossed flexures and a lateral wire. The lateral wire basically
connects two linkages. The crossed flexure enables the joint to
be robust to compressive force. A joint without a flexure tends
to deviate from the center when compressive force is exerted
as shown in Fig. 6 (c). The crossed flexure, however, prevents
the joint from deviating, as can be seen in Fig. 6 (b).
D. Height-Adjustable Triggering Mechanism
The second design requirement is active release of stored
energy to control take-off speed of jumping. The mechanism
in Fig. 7 consists of a winding pulley gear, a planet gear and a
motor gear. The planet gear rotates around the motor gear and
contacts and detaches from the winding pulley gear depending
on rotational direction of the motor gear. When the motor
rotates clockwise, the planet gear contacts the winding pulley
gear and starts to wind the wires. When the motor rotates
counter-clockwise, the planet gear detaches from the winding
pulley gear, and the winding pulley gear is released. With this
active triggering mechanism, the jumping module can be
released at any state, as shown in Fig. 4, which enables control
of the take-off speed of jumping.
III. INTEGRATED JUMPING-CRAWLING ROBOT
The jumping module is integrated with a lightweight Dash
crawler. The crawler has a vacant space inside its body of 100
mm length x 20 mm width x 35 mm depth. The jumping
module is installed inside the crawler as shown in Fig. 8.
The jump-crawler’s stored elastic energy is adjusted
according to the target take-off speed of jumping. When the
robot needs to jump high, the motor fully winds the pulley
wires to store more elastic energy, as shown in Fig. 8 (a). When
the robot needs to make a low jump, the motor winds the wires
less, and the jumping module is only partially compressed, as
shown in Fig. 8 (b). When the module is compressed to less
than 35 mm, the jumping structure does not touch the ground
at all, and the robot can crawl as normal.
(a)
(b)
(c)
Fig. 6. Knee-inspired roll and slide joint. (a) From the flat state to the
fully folded state. Joints in compressive force of 35N (b) with cross
flexures and (c) without cross flexures.
Fig. 7. (a), (b) Conceptual diagram of the active triggering mechanism
using a single DC motor. (c), (d) Magnified 3D CAD view of the
triggering mechanism.
Fig. 5. (a) The jumping module in (a) the state of fully stored energy
and (b) the released state. (c) 3D CAD model of the entire jumping
module. (d) Latex rubber routing.
Fig. 8. Conceptual model of the height-adjustable integrated crawling-
jumping robot, showing the state of the mechanism for (a) high jumps
and (b) low jumps.
The diamond structure of the jumping module is located at
the center of the robot, which distributes the mass distribution
to reduce rotational motion when the robot jumps. The mass
budget of whole system is given in Table Ⅲ.
The robot is controlled by the dsPIC33JF128MC706-based
board [17]. The board uses an 802.15.4 wireless radio and two
H-bridge motor controller. The crawler uses two 7 mm-
diameter, 3.3 Ω brushed DC motors (Didel MK07-3.3) and is
controlled by changing the PWM ratio. The jumping module
uses a DC motor (Pololu 1000:1 gear ratio) and a simple
direction control is applied to store and release the energy.
IV. MODELING
To investigate how much force is required to load the
proposed jumping mechanism, we created a static model.
Using this model, the required loading force according to the
shape of the jumping module is calculated.
Also, the jumping dynamics is analyzed based on the
Lagrangian formulation. The process of jumping is completed
within only 30 ms. Therefore, dynamics should be considered
to precisely examine how the mechanism works. Based on the
dynamic model, the take-off time, velocity, and energy used
for jumping can be calculated.
A. Loading Force Analysis
To select the actuator to load the mechanism, a static
loading force analysis is performed. Fig. 9 shows the model of
the proposed mechanism. The model represents the routed
latex rubber as six symmetrically positioned springs in the
upper triangle and the lower triangle, as shown in Fig. 9. The
three springs in each triangle have the spring constant of k1, k2
and k3, which are determined by tensile tests. The loading force,
F, can be calculated based on the moment equilibrium
equation as follows:
𝑟𝐹𝑠𝑖𝑛𝜃′ = 𝑟1𝑘1𝛥𝑥1𝑐𝑜𝑠𝜃′ + 𝑟2𝑘2𝛥𝑥2𝑐𝑜𝑠𝜃′ +
𝑟3𝑘3𝛥𝑥3𝑐𝑜𝑠𝜃′ (1)
where 𝛥𝑥𝑖 = 𝑟𝑖(𝑠𝑖𝑛𝜃′ − 𝑠𝑖𝑛𝜃𝑖𝑛𝑖𝑡𝑖𝑎𝑙′ ) , 𝜃′ = 𝜃1/2 and
𝜃𝑖𝑛𝑖𝑡𝑖𝑎𝑙′ = 𝜃1,𝑖𝑛𝑖𝑡𝑖𝑎𝑙/2
𝐹 = 8(𝑟1
2𝑘1+𝑟22𝑘2+𝑟3
2𝑘3)(𝑠𝑖𝑛𝜃′−𝑠𝑖𝑛𝜃𝑖𝑛𝑖𝑡𝑖𝑎𝑙′ )𝑐𝑜𝑠𝜃′
𝑟𝑠𝑖𝑛𝜃′ (2)
where 𝑟1 = 41𝑚𝑚 , 𝑟2 = 36𝑚𝑚 , 𝑟3 = 31𝑚𝑚 , 𝑟 = 45𝑚𝑚 ,
𝑘1 = 172.86𝑁/𝑚 , 𝑘2 = 200.14𝑁/𝑚, 𝑘3 = 216.5𝑁/𝑚 and
𝜃𝑖𝑛𝑖𝑡𝑖𝑎𝑙′ = 20˚.
Based on eq. (2), the relation between the loading force and
the angle, θ1, is given in Fig. 10. In this figure, the peak loading
force is 77.0 N. Given that the stall torque of the DC motor is
0.9 Nm, the radius of the pulley should not exceed 11.6 mm as
follows:
𝑃𝑢𝑙𝑙𝑒𝑦_𝑟𝑎𝑑𝑖𝑢𝑠𝑚𝑎𝑥 = τ/𝐹𝑝𝑒𝑎𝑘 = 0.900Nm/77.0N = 11.6 mm
(3)
The pulley used in the mechanism has a radius of 2 mm and
produces enough force for loading.
B. Dynamics
The model consists of five rigid links and four rotational
joint. To analyze the dynamics, two variables (𝜃1 and 𝜃0) are
used to indicate the position of each link. The model is a one-
degree-of-freedom system and has a generalized coordinate of
the body angle, 𝜃1. The position of the links is given as follows:
��1 = [
1
2𝑟 cos 𝜃0
1
2𝑟 cos 𝜃0
] (4)
Fig. 10. Loading force vs. angle.
TABLE III. MASS BUDGET
Components Mass (g)
Jumper transmission 4.8
Carbon rods (8 ea) 2.0
Joints (8 ea) 4.0
Wire, joint rubber 2.2
Jumper motor 11.0
Latex rubber for energy storage (2 ea) 2.2
Control board 6.9
Li-Po Battery 5.3
Crawler body 16.0
Crawler transmission 5.0
Total 59.4
Fig. 9. Dynamic model of the proposed mechanism. G5 and G6
indicate the payload such as a battery, electronics, and an actuator.
��2 = [𝑟 cos 𝜃0 +
1
2𝑟 cos (𝜃0 + 𝜃1)
𝑟 sin 𝜃0 +1
2𝑟 sin (𝜃0 + 𝜃1)
] (5)
��3 = [𝑟 cos (𝜃0 + 𝜃1) +
1
2𝑟 cos 𝜃0
𝑟 sin (𝜃0 + 𝜃1) +1
2𝑟 cos 𝜃0
] (6)
��4 = [
1
2𝑟 cos (𝜃0 + 𝜃1)
1
2𝑟 sin (𝜃0 + 𝜃1)
] (7)
��5 =
[ 𝑟 cos 𝜃0 +
1
2𝑟 cos(𝜃0 + 𝜃1) −
𝑟5,𝑦 cos (𝜃0 +1
2𝜃1) − 𝑟5,𝑥sin (𝜃0 +
1
2𝜃1)
𝑟 sin 𝜃0 +1
2𝑟 sin(𝜃0 + 𝜃1) +
𝑟5,𝑦 sin (𝜃0 +1
2𝜃1) + 𝑟5,𝑥cos (𝜃0 +
1
2𝜃1) ]
(8)
��6 =
[ 𝑟 cos 𝜃0 +
1
2𝑟 cos(𝜃0 + 𝜃1) −
𝑟6,𝑦 cos (𝜃0 +1
2𝜃1) + 𝑟6,𝑥sin (𝜃0 +
1
2𝜃1)
𝑟 sin 𝜃0 +1
2𝑟 sin(𝜃0 + 𝜃1) +
𝑟6,𝑦 sin (𝜃0 +1
2𝜃1) − 𝑟6,𝑥cos (𝜃0 +
1
2𝜃1) ]
(9)
where Gi is the position of links, r is the length of each link of
the diamond-shaped body, r5,x, r5,y, r6,x, and r6,y are the
distance to added masses.
𝜃1 is the angle of the diamond. 𝜃1 and 𝜃0 have the
following relationship:
𝜃0 = (180° − 𝜃1)/2 (10)
With the positions and the kinematic constraints, the
dynamics of the jumping module are numerically solved by a
Lagrange formulation. The initial conditions are set as follows:
𝜃1 = 170° at fully stored state (11)
Take-off of the jumping mechanism occur when the
vertical reaction force, V(t) in (13), is zero.
𝑚𝑟𝑜𝑏𝑜𝑡𝑎𝑟𝑜𝑏𝑜𝑡,𝑥 = ∑ 𝑚𝑖𝑎𝑖,𝑥(𝑡) = −𝐻(𝑡)6𝑖=1 (12)
𝑚𝑟𝑜𝑏𝑜𝑡𝑎𝑟𝑜𝑏𝑜𝑡,𝑦 = ∑ 𝑚𝑖𝑎𝑖,𝑦(𝑡) = 𝑉(𝑡)6𝑖=1 − ∑ 𝑚𝑖𝑔
6𝑖=1 (13)
where mrobot is the total mass of the robot, arobot is the
acceleration of the robot’s center of mass, ai is the acceleration
of each link, and H is the horizontal reaction force on the
ground. Also, the take-off translational velocity, (14), and the
angular velocity, (15), are determined as follows:
𝑚𝑟𝑜𝑏𝑜𝑡𝑣𝑟𝑜𝑏𝑜𝑡 = ∑ 𝑚𝑖𝑣𝑖,𝑓6𝑖=1 (14)
𝑚𝑟𝑜𝑏𝑜𝑡𝑤𝑟𝑜𝑏𝑜𝑡 = ∑ 𝑚𝑖𝑤𝑖,𝑓6𝑖=1 (15)
where vrobot is the velocity of the robot’s center of mass and
wrobot is the angular velocity of the robot. vi,f is the translational
velocity, and wi,f is the angular velocity of each link just before
takeoff.
V. EXPERIMENTAL RESULTS
The jumping module is designed to satisfy two design
requirements: Large energy-storing capacity and height-
adjustable triggering. To examine the functionality of the
jumping module, we test jumping by varying the quantity of
stored energy in the jumping module and integrated jumping-
crawling by adjusting different take-off and crawling speeds.
To operate the robot, a LiPo battery (3.7V, 370mAh) is used.
The jumping mechanism requires 240mA for 28s to fully
charge the jumping energy and the crawler consumes about
600mA continuously.
A. Jumping Experiment
The jumping experiments are done by varying the quantity
of stored energy. Fig. 11 shows high-speed images and
corresponding dynamic models of jumping at two different
initial states. In Fig. 11 (a) the module initially has 1.39 J of
elastic energy, and in Fig. 11 (b) it has 0.49 J.
In Fig. 11 (a), the jumping module takes off within 22.4 ms
with a speed of 7.71 m/s and jumps to 2.90 m. The module
actually uses 1.1 J, which is 79% of its initially stored energy.
The jumping module in Fig. 11 (b) initially stores 0.49 J and
uses 0.39 J which is 79% of its initially stored energy. The
module takes off within 8.40 ms with a speed of 4.49 m/s and
jumps up to 1.10 m.
Table 2 compares data from the experiment and the model.
Both sets of data shows similar values but have slight
differences in the conversion efficiency, which is the ratio of
Fig. 11. High-speed (5000 fps) image of the jumping module and visualizatin of dynamic modeling of its movements. The red arrow indicates the
direction of reaction force from the ground.
TABLE IV. COMPARISON OF EXPERIMENT AND MODELING
- High jumps Low jumps
Model Exp. Model Exp.
Take-off time (ms) 23.8 22.4 7.80 8.40
Take-off speed (m/s) 7.81 7.71 4.57 4.49
Initially stored energy (J) 1.39 1.39 0.49 0.49
Actual used energy (J) 1.16 1.1 0.40 0.39
Conversion efficiency (%)* 83 79 82 79
Jumping height (m) - 2.90 - 1.10
*Conversion efficiency is the ratio of initially stored energy to actual
kinetic energy at take-off [3], [13].
the initially stored energy to the actual used energy. This error
may come from a small degree of hysteresis in the latex rubber
since the latex is modeled as a perfect linear spring for
simplicity.
B. Integrated Jumping-Crawling Experiments
The integrated jumping-crawling robot is tested by varying
crawling speed and take-off speed. Fig. 12 (a) shows the robot
with crawling speed of 0.63 m/s and take-off speed of 4.52 m/s.
This combined motion enables the robot to jump 1.10 m and
overcome 0.80 m high obstacle.
Fig. 12 (b) shows the horizontal and vertical distances
achieved in three different cases. In case 3, when the robot has
a crawling speed of 0 m/s and a take-off speed of 5.60 m/s, it
jumps nearly vertically. In case 1 and 2, the robot moves with
almost equal crawling speed but different take-off speeds. In
case 1 the robot’s jumping module has 0.98 J of initially stored
energy and jumps to 1.10 m. In case 2, the fully loaded
jumping module has 1.39 J of stored energy, and jumps to 1.62
m. In the horizontal direction, in cases 1 and 2 the robot
crawled 0.48 m and 0.60 m, respectively. The robot has an
average horizontal moving speed in cases 1 and 2 of 0.57 m/s
and 0.59 m/s, respectively, which means that crawling speed
and take-off speed are independently controlled.
VI. CONCLUSION
In this paper, we propose a trajectory-controlled integrated
jumping-crawling robot. To this end, a novel jumping module
is developed with a large energy-storing capacity and a height-
adjustable active trigger. To increase the energy-storing
capacity, the jumping module incorporates latex rubber and
knee-like joints. These components enables the jumping
module to utilize large displacement of material, which is our
strategy for maximizing energy-storing capacity. Also, a novel
active trigger is designed to release the stored energy at any
state. The trigger uses only a single DC motor and works by
controlling the direction of rotation. With this trigger, the
jumping module can control its jumping height. The developed
jumping module is integrated with a lightweight Dash crawler.
The whole system weighs 59.4 g and achieves different
trajectories by controlling crawling speed and take-off speed.
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Fig 12. (a) Integrated jumping-crawling to overcome an 80-cm
obstacle. (b)Vertical and horizontal distance of the integrated
jumping-crawling robot. Numbers in the figure key are crawling speed
and take-off speed. The time between dots is 0.168s.